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A simple model of global cascades on random hypergraphs

Author

Listed:
  • Chen, Lei
  • Zhu, Yanpeng
  • Zhu, Jiadong
  • Cui, Longqing
  • Ruan, Zhongyuan
  • Small, Michael
  • Christensen, Kim
  • Liu, Run-Ran
  • Meng, Fanyuan

Abstract

This study introduces a comprehensive framework that situates information cascades within the domain of higher-order interactions, utilizing a double-threshold hypergraph model. We propose that individuals (nodes) gain awareness of information through each communication channel (hyperedge) once the number of information adopters surpasses a threshold ϕm. However, actual adoption of the information only occurs when the cumulative influence across all communication channels exceeds a second threshold, ϕk. We analytically derive the cascade condition for both the case of a single seed node using percolation methods and the case of any seed size employing mean-field approximation. Our findings underscore that when considering the fractional seed size, r0∈(0,1], the connectivity pattern of the random hypergraph, characterized by the hyperdegree, k, and cardinality, m, distributions, exerts an asymmetric impact on the global cascade boundary. This asymmetry manifests in the observed differences in the boundaries of the global cascade within the (ϕm,〈m〉) and (ϕk,〈k〉) planes. However, as r0→0, this asymmetric effect gradually diminishes. Overall, by elucidating the mechanisms driving information cascades within a broader context of higher-order interactions, our research contributes to theoretical advancements in complex systems theory.

Suggested Citation

  • Chen, Lei & Zhu, Yanpeng & Zhu, Jiadong & Cui, Longqing & Ruan, Zhongyuan & Small, Michael & Christensen, Kim & Liu, Run-Ran & Meng, Fanyuan, 2025. "A simple model of global cascades on random hypergraphs," Chaos, Solitons & Fractals, Elsevier, vol. 193(C).
  • Handle: RePEc:eee:chsofr:v:193:y:2025:i:c:s0960077925000943
    DOI: 10.1016/j.chaos.2025.116081
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    References listed on IDEAS

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    1. repec:plo:pone00:0078433 is not listed on IDEAS
    2. Ke, Xingfu & Wen, Youjin & Yu, Hao & Meng, Fanyuan, 2024. "A simple model of global cascades in signed networks," Chaos, Solitons & Fractals, Elsevier, vol. 186(C).
    3. Guilherme Ferraz de Arruda & Giovanni Petri & Pablo Martin Rodriguez & Yamir Moreno, 2023. "Multistability, intermittency, and hybrid transitions in social contagion models on hypergraphs," Nature Communications, Nature, vol. 14(1), pages 1-15, December.
    4. Wang, Jiajia & Zhao, Laijun & Huang, Rongbing, 2014. "SIRaRu rumor spreading model in complex networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 398(C), pages 43-55.
    5. Zhao, Laijun & Wang, Jiajia & Chen, Yucheng & Wang, Qin & Cheng, Jingjing & Cui, Hongxin, 2012. "SIHR rumor spreading model in social networks," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 391(7), pages 2444-2453.
    6. Duncan J. Watts & Peter Sheridan Dodds, 2007. "Influentials, Networks, and Public Opinion Formation," Journal of Consumer Research, Journal of Consumer Research Inc., vol. 34(4), pages 441-458, May.
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